Notice that \(Z_k\)  is a 4-dimensional 1-handlebody and the pairwise intersections \(X_i\cap X_j\)  are 3-dimensional handlebodies of genus \(g\) . This definition is just a slightly more technical rewording of the original presented at the beginning of the section. In [1]}, Gay and Kirby generalize this definition to allow 4-manifolds which have surface bundles over \(S^1\)  as boundary. We will again present this definition by presenting the wedges of the trisection as thickened 3-dimensional pieces.
